Porous fluoropolymer membranes having a large number of continuous fine pores are known. Such materials have been extensively employed as filters because of the fact that fluoropolymers, and particularly polytetrafluoroethylene (PTFE) are known to have high heat resistance and chemical resistance. However, they cannot be applied to separation of particles dispersed in water due to their high liquid water repellency and low liquid water permeability. In other words, they are hydrophobic in nature. In order to provide such hydrophobic porous fluorine membranes with a capability of permeating water therethrough, it is necessary to make inner surfaces of the fine pores of the materials hydrophilic. Review has been made of various methods for making the inner surface of the fine pores of the porous fluoropolymer membrane hydrophilic. Such methods may include, for example, (1) the method of replacement with water after impregnation of the membrane with a hydrophilic organic solvent such as an alcohol; (2) the method of impregnating the membrane with a surfactant through its alcohol solution; (3) the method of impregnating the membrane with a monomer containing a hydrophilic group and then polymerizing the monomer; (4) the method of making the membrane hydrophilic by impregnation with a hydrophilic polymer such as polyvinyl alcohol through its aqueous solvent solution; (5) the method of impregnating the membrane with a monomer containing a hydrophilic group and then graft-polymerizing the monomer by treatment with strong reducing agents or plasma gases, or by irradiation of high energy radiation such as a gamma ray, an electron beam, etc. These conventional methods, however, have various drawbacks. The method (1) has the problem that the effect of replacement with water is lost once the materials have been dried. The method (2) has the drawback that the surfactant may likely elute thereby worsening durability. The methods (3) and (4) may have the likelihood to clog up the fine pores of the materials and have the drawback that the polymer may be likely to elute and their durabilities are poor. Consequently, the cross-linking or crystallizing treatments of the impregnated polymer of the surfactant are sometimes carried out for the propose of the preventing of the elution of the polymer in the methods (2), (3) and (4). These treatments are described in examined Japanese Patent Publication Nos. 21270/1978, 8869/1979. 154737/1981 and 98640/1989. The method (5) may deteriorate the mechanical properties of the materials and it may be difficult to prevent homopolymerization of the monomer and the elution of the homopolymer.